Effects of back reaction in the Brans-Dicke-dilaton cosmology

The effects of back reaction are studied in the Brans-Dicke-dilaton cosmology in four-dimensional spacetime. In particular, the extended inflationary model is examined by taking account of the effect of back reaction. As quantized matter, conformally invariant quantum fields are considered. In conformally flat spacetime, the expectation value of the stress tensor is exactly calculable. Cosmological solutions are studied in the radiation-dominated and nonvanishing cosmological constant universes. The most important contributions come from the trace-anomaly part of the stress tensor. In most of the parameter region and boundary conditions, solutions behave quite differently from the classical solutions even for the late period of the big bang. Only by fine-tuning the boundary conditions are solutions obtained whose behaviors are close to the classical ones. The sign of the fourth-derivative term of the scale factor in the stress tensor is very important, and it determines whether or not stable solutions exist